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3 years ago

andres has 10 more goldfish than todd. Together,they have 50 goldfish.How many goldfish does each boy have?

2 answers:

5 0

Let Todd's fish = T

that would make

Andres fish = T + 10.

Together they have 50 fish so...
T + (T +10) = 50
2T + 10 = 50
2T = 40
T = 20

so Todd has 20 fish.

Remember Andres has
T + 10 fish, so...

T + 10 =
20 + 10 = 30

Andres has 30 fish

Check the problem by plugging the numbers into the original equation...

T + T + 10 = 50
20 + 20 + 10 = 50
50 = 50

It checks!

Dmitry [639]3 years ago

3 0

Let's go ahead and construct an equation to show this. Together, they have 50 goldfish. This can be represented as =50.

Since we don't know how many Todd has, we're going to make a variable. We'll name it T, for Todd.

What about Andres? How many does he have? 10 more than Todd. Well, if Todd's amount is T, and Andres has 10 more, we can express that as T+10.

Now, just put the two pieces together! T+10=50.

The next step is inverse operations. You want to find out how many T is, so you need to get rid of the 10. To take 10 away from something is doing what? Subtraction! Be warned, though; whatever you do to one side of the problem, you have to do to the other. 10-10 is 0, and 50-10 is 40. Since we took the 10 away and 50 is now 40, what you're left with is T=40.

Wait a second.. wasn't "T" Todd's amount? Yep! That means that Todd has 40 goldfish. And we already know that Andres has 10, so there's your answer!

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A palm tree casts a shadow that is 28 feet long. A 6-foot sign casts a shadow 8 feet long.

s2008m [1.1K]

Answer: The height of the palm tree is 21 feet.

Step-by-step explanation:

We can use a ratio to solve this:

Actual height to shadow for both objects. The fraction equivalents must be equal.

6/8 = x/28 . Cross multiply

6(28) = 8x

168 = 8x Divide both sides by 8 (8's "cancel" on the right)

168/8 =8x/8

21 = x . This gives us the tree's height as 21 feet.

Another way to solve this is to use the ratios, but simplify the first fraction

6/8 = 3/4

Then multiply the length of the shadow by 3/4

3/4 × 28 = height

28÷4 = 7 7 × 3 = 21

21 feet= the height of the palm tree.

3 0

3 years ago

Translate this sentence into an equation. 62 is the sum of 12 and Chrissy's age. Use the variable c to represent Chrissy's age.

Greeley [361]

62= 12+c

Which your answer is 50 cause if you take 62 and subtract it to 12 it's 50. So 50 + 12 = 62

5 0

4 years ago

The cost to rent a car is $25 plus an additional $0.15 for each mile the car is driven. Which of the following equations could b

Nastasia [14]

Answer:

0.15m+25=c

replace c with 71.50

the third one

25+0.15m=71.8

3 0

3 years ago

Read 2 more answers

Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe

ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for $n\geq 78$

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: $\sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4$

For n=1: $\sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4$

From this point we will assume that $n\geq 2$

As we can see, $\sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4$ and $(4n)^4=256n^4$ . Then,

$\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4$

Now, we will use the formula for the sum of the first 4th powers:

$\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}$

Therefore:

$\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0$

and, because $n \geq 0$ ,

$465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1$